Stellar granulation as seen in disk-integrated intensity. I. Simplified theoretical modeling

The solar granulation is known for a long time to be a surface manifestation of convection. Thanks to the current space-borne missions CoRoT and Kepler, it is now possible to observe in disk-integrated intensity the signature of this phenomena in a growing number of stars. The space-based photometric measurements show that the global brightness fluctuations and the lifetime associated with granulation obeys characteristic scaling relations. We thus aim at providing a simple theoretical modeling to reproduce these scaling relations and subsequently at inferring the physical properties of granulation properties across the HR diagram. We develop a simple 1D theoretical model that enable us to test any prescription concerning the time-correlation between granules. The input parameters of the model are extracted from 3D hydrodynamical models of the surface layers of stars, and the free parameters involved in the model are calibrated with solar observations. Two different prescriptions for representing the eddy time-correlation in the Fourier space are compared: a Lorentzian and an exponential form. Finally, we compare our theoretical prediction with a 3D radiative hydrodynamical (RHD) numerical modeling of stellar granulation (ab-initio approach). Provided that the free parameters are appropriately adjusted, our theoretical model satisfactorily reproduces the shape and the amplitude of the observed solar granulation spectrum. The best agreement is obtained with an exponential form. Furthermore, our theoretical model results in granulation spectra that consistently agree with the these calculated on the basis of the ab-initio approach with two 3D RHD models. Comparison between theoretical granulation spectra calculated with the present model and high precision photometry measurements of stellar granulation is undertaken in a companion paper.Comment: 10 pages, 2 figures, accepted for publication in A&

The Uniqueness Problem of Sequence Product on Operator Effect Algebra ε(H)\varepsilon (H)

A quantum effect is an operator on a complex Hilbert space $H$ that satisfies $0\leq A\leq I$. We denote the set of all quantum effects by ${\cal E}(H)$. In this paper we prove, Theorem 4.3, on the theory of sequential product on ${\cal E}(H)$ which shows, in fact, that there are sequential products on ${\cal E}(H)$ which are not of the generalized L\"{u}ders form. This result answers a Gudder's open problem negatively

The effects of numerical resolution on hydrodynamical surface convection simulations and spectral line formation

The computationally demanding nature of radiative-hydrodynamical simulations of stellar surface convection warrants an investigation of the sensitivity of the convective structure and spectral synthesis to the numerical resolution and dimension of the simulations, which is presented here. With too coarse a resolution the predicted spectral lines tend to be too narrow, reflecting insufficient Doppler broadening from the convective motions, while at the currently highest affordable resolution the line shapes have converged essentially perfectly to the observed profiles. Similar conclusions are drawn from the line asymmetries and shifts. In terms of abundances, weak FeI and FeII lines show a very small dependence (~0.02 dex) while for intermediate strong lines with significant non-thermal broadening the sensitivity increases (~0.10 dex). Problems arise when using 2D convection simulations to describe an inherent 3D phenomenon, which translates to inaccurate atmospheric velocity fields and temperature and pressure structures. In 2D the theoretical line profiles tend to be too shallow and broad compared with the 3D calculations and observations, in particular for intermediate strong lines. In terms of abundances, the 2D results are systematically about 0.1 dex lower than for the 3D case for FeI lines. Furthermore, the predicted line asymmetries and shifts are much inferior in 2D. Given these shortcomings and computing time considerations it is better to use 3D simulations of even modest resolution than high-resolution 2D simulations.Comment: Accepted for A&

Is the Sun Lighter than the Earth? Isotopic CO in the Photosphere, Viewed through the Lens of 3D Spectrum Synthesis

We consider the formation of solar infrared (2-6 micron) rovibrational bands of carbon monoxide (CO) in CO5BOLD 3D convection models, with the aim to refine abundances of the heavy isotopes of carbon (13C) and oxygen (18O,17O), to compare with direct capture measurements of solar wind light ions by the Genesis Discovery Mission. We find that previous, mainly 1D, analyses were systematically biased toward lower isotopic ratios (e.g., R23= 12C/13C), suggesting an isotopically "heavy" Sun contrary to accepted fractionation processes thought to have operated in the primitive solar nebula. The new 3D ratios for 13C and 18O are: R23= 91.4 +/- 1.3 (Rsun= 89.2); and R68= 511 +/- 10 (Rsun= 499), where the uncertainties are 1 sigma and "optimistic." We also obtained R67= 2738 +/- 118 (Rsun= 2632), but we caution that the observed 12C17O features are extremely weak. The new solar ratios for the oxygen isotopes fall between the terrestrial values and those reported by Genesis (R68= 530, R6= 2798), although including both within 2 sigma error flags, and go in the direction favoring recent theories for the oxygen isotope composition of Ca-Al inclusions (CAI) in primitive meteorites. While not a major focus of this work, we derive an oxygen abundance of 603 +/- 9 ppm (relative to hydrogen; 8.78 on the logarithmic H= 12 scale). That the Sun likely is lighter than the Earth, isotopically speaking, removes the necessity to invoke exotic fractionation processes during the early construction of the inner solar system

A simulation of solar convection at supergranulation scale

We present here numerical simulations of surface solar convection which cover a box of 30$\times30\times$3.2 Mm$^3$ with a resolution of 315$\times315\times$82, which is used to investigate the dynamics of scales larger than granulation. No structure resembling supergranulation is present; possibly higher Reynolds numbers (i.e. higher numerical resolution), or magnetic fields, or greater depth are necessary. The results also show interesting aspects of granular dynamics which are briefly presented, like extensive p-mode ridges in the k-$\omega$ diagram and a ringlike distribution of horizontal vorticity around granules. At large scales, the horizontal velocity is much larger than the vertical velocity and the vertical motion is dominated by p-mode oscillations.Comment: Contribution to the proceedings of the workshop entitled "THEMIS and the new frontiers of solar atmosphere dynamics" (March 2001), 6 pages, to appear in Nuovo Cimento

Spiral-grooved shaft seals substantially reduce leakage and wear

Rotating shaft seals used in space power systems have spiral grooves in one or both of the opposing seal faces. These grooves induce a pumping action which displaces the intervening fluid radially inward toward the shaft and counters the centrifugal forces which tend to displace the fluid outward

6Li detection in metal-poor stars: can 3D model atmospheres solve the second lithium problem?

The presence of 6Li in the atmospheres of metal-poor halo stars is usually inferred from the detection of a subtle extra depression in the red wing of the 7Li doublet line at 670.8 nm. However, the intrinsic line asymmetry caused by convective flows in the photospheres of cool stars is almost indistinguishable from the asymmetry produced by a weak 6Li blend on a (presumed) symmetric 7Li profile. Previous determinations of the 6Li/ 7Li isotopic ratio based on 1D model atmospheres, ignoring the convection-induced line asymmetry, must therefore be considered as upper limits. By comparing synthetic 1D LTE and 3D non-LTE line profiles of the Li 670.8 nm feature, we quantify the differential effect of the convective line asymmetry on the derived 6Li abundance as a function of effective temperature, gravity, and metallicity. As expected, we find that the asymmetry effect systematically reduces the resulting 6Li/7Li ratios. Depending on the stellar parameters, the 3D-1D offset in 6Li/7Li ranges between -0.005 and -0.020. When this purely theoretical correction is taken into account for the Asplund 2006 sample of stars, the number of significant 6Li detections decreases from 9 to 5 (2 sigma criterion), or from 5 to 2 (3 sigma criterion). We also present preliminary results of a re-analysis of high-resolution, high S/N spectra of individual metal-poor turn-off stars, to see whether the "second Lithium problem" actually disappears when accounting properly for convection and non-LTE line formation in 3D stellar atmospheres. Out of 8 stars, HD84937 seems to be the only significant (2 sigma) detection of 6Li. In view of our results, the existence of a 6Li plateau appears questionable.Comment: To appear in the proceedings of 'Lithium in the Cosmos', Paris, Feb. 27-29, 2012, Memorie della Societa' Astronomica Italiana Supplement

(Conformal) Killing vectors and their associated bivectors

Fayos and Sopuerta have recently set up a formalism for studying vacuum spacetimes with an isometry, a formalism that is centred around the bivector corresponding to the Killing vector and that adapts the tetrad to the bivector. Steele has generalized their approach to include the homothetic case. Here, we generalize this formalism to arbitrary spacetimes and to homothetic and conformal Killing vectors but do not insist on aligning the tetrad with the bivector. The most efficient way to use the formalism to find conformal Killing vectors (proper or not) of a given spacetime is to combine it with the notion of a preferred tetrad. A metric by Kimura is used as an illustrative example

Surface-effect corrections for solar-like oscillations using 3D hydrodynamical simulations

The space-borne missions have provided us with a wealth of high-quality observational data that allows for seismic inferences of stellar interiors. This requires the computation of precise and accurate theoretical frequencies, but imperfect modeling of the uppermost stellar layers introduces systematic errors. To overcome this problem, an empirical correction has been introduced by Kjeldsen et al. (2008, ApJ, 683, L175) and is now commonly used for seismic inferences. Nevertheless, we still lack a physical justification allowing for the quantification of the surface-effect corrections. We used a grid of these simulations computed with the CO$^5$BOLD code to model the outer layers of solar-like stars. Upper layers of the corresponding 1D standard models were then replaced by the layers obtained from the horizontally averaged 3D models. The frequency differences between these patched models and the 1D standard models were then calculated using the adiabatic approximation and allowed us to constrain the Kjeldsen et al. power law, as well as a Lorentzian formulation. We find that the surface effects on modal frequencies depend significantly on both the effective temperature and the surface gravity. We further provide the variation in the parameters related to the surface-effect corrections using their power law as well as a Lorentzian formulation. Scaling relations between these parameters and the elevation (related to the Mach number) is also provided. The Lorentzian formulation is shown to be more robust for the whole frequency spectrum, while the power law is not suitable for the frequency shifts in the frequency range above $\nu_{\rm max}$.Comment: 11 pages, 14 figures, 4 tables; accepted for publication in Astronomy & Astrophysic